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   <div id="projectname">Calico
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   <div id="projectbrief">A visual-inertial calibration library designed for rapid problem construction and debugging.</div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef CALICO_BSPLINE_H_</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor">#define CALICO_BSPLINE_H_</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160; </div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &quot;calico/typedefs.h&quot;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160; </div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &quot;absl/status/statusor.h&quot;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &quot;ceres/problem.h&quot;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &quot;Eigen/Dense&quot;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160; </div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160; </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacecalico.html">calico</a> {</div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="comment">// Generic N-DOF spline fitter. This class implements the following paper:</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="comment">// &quot;General Matrix Representations for B-Splines&quot;, K. Qin.</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="comment">// https://xiaoxingchen.github.io/2020/03/02/bspline_in_so3/general_matrix_representation_for_bsplines.pdf</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160;<span class="keyword">template</span> &lt;<span class="keywordtype">int</span> N, <span class="keyword">typename</span> T = <span class="keywordtype">double</span>&gt;</div>
<div class="line"><a name="l00017"></a><span class="lineno"><a class="line" href="classcalico_1_1BSpline.html">   17</a></span>&#160;<span class="keyword">class </span><a class="code" href="classcalico_1_1BSpline.html">BSpline</a> {</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160; </div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;  ~<a class="code" href="classcalico_1_1BSpline.html">BSpline</a>() = <span class="keywordflow">default</span>;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160; </div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;  <span class="comment">// Add this spline&#39;s control points to a ceres problem. Returns the number of</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;  <span class="comment">// parameters added, which should be N * number of control points.</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;  <span class="keywordtype">int</span> AddParametersToProblem(ceres::Problem&amp; problem);</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160; </div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;  <span class="comment">// Fits an N-DOF uniform B-spline fitted to given timestamps</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;  <span class="comment">// and N-dimensional data. User also specifies the spline order and the knot</span></div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;  <span class="comment">// frequency of the spline.</span></div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;  absl::Status FitToData(<span class="keyword">const</span> std::vector&lt;T&gt;&amp; time,</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;                         <span class="keyword">const</span> std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt;&amp; data,</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;                         <span class="keywordtype">int</span> spline_order, T knot_frequency);</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;  <span class="comment">// Convenience function for getting the index of the active spline segement for</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;  <span class="comment">// a queried time.</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;  <span class="keywordtype">int</span> GetSplineIndex(T query_time) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;  <span class="comment">// Convenience function for getting the index of the appropriate beginning</span></div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;  <span class="comment">// knot for a spline segment with index control_point_index.</span></div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;  <span class="keywordtype">int</span> GetKnotIndexFromSplineIndex(<span class="keywordtype">int</span> control_point_index) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160; </div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;  <span class="comment">// Getter for the spline order.</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;  <span class="keywordtype">int</span> GetSplineOrder() <span class="keyword">const</span>;</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;  <span class="comment">// Interpolate the spline at given times for the given derivative. If no</span></div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;  <span class="comment">// derivative is specified, it defaults to direct interpolation.</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;  absl::StatusOr&lt;std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt;&gt;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;  Interpolate(<span class="keyword">const</span> std::vector&lt;T&gt;&amp; times, <span class="keywordtype">int</span> derivative = 0) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160; </div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;  <span class="comment">// TODO(yangjames): Description</span></div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;  Eigen::MatrixX&lt;T&gt;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;  GetSplineBasis(<span class="keywordtype">int</span> spline_idx, T stamp, <span class="keywordtype">int</span> derivative) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160; </div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;  <span class="keyword">static</span> Eigen::Vector&lt;T, N&gt; Evaluate(</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;      <span class="keyword">const</span> Eigen::Ref&lt;<span class="keyword">const</span> Eigen::MatrixX&lt;T&gt;&gt;&amp; control_points_set, T knot0,</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;      T knot1, <span class="keyword">const</span> Eigen::MatrixX&lt;T&gt;&amp; basis_matrix, T stamp, <span class="keywordtype">int</span> derivative);</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160; </div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;  <span class="comment">// Setter/getter for knot vector.</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;  <span class="keyword">const</span> std::vector&lt;T&gt;&amp; knots()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> knots_; }</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;  std::vector&lt;T&gt;&amp; knots() { <span class="keywordflow">return</span> knots_; }</div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160; </div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;  <span class="comment">// Setter/getter for control points.</span></div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;  <span class="keyword">const</span> std::vector&lt;Eigen::Vector&lt;T, N&gt;&gt;&amp; control_points()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;    <span class="keywordflow">return</span> control_points_;</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;  }</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;  std::vector&lt;Eigen::Vector&lt;T, N&gt;&gt;&amp; control_points() {</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;    <span class="keywordflow">return</span> control_points_;</div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;  }</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;  <span class="comment">// Setter/getter for basis matrices.</span></div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;  <span class="keyword">const</span> std::vector&lt;Eigen::MatrixX&lt;T&gt;&gt;&amp; basis_matrices()<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;    <span class="keywordflow">return</span> Mi_;</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;  }</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;  std::vector&lt;Eigen::MatrixX&lt;T&gt;&gt;&amp; basis_matrices() {</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;    <span class="keywordflow">return</span> Mi_;</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;  }</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160; </div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;  <span class="comment">// Data/parameters for fitting spline.</span></div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;  <span class="keywordtype">int</span> spline_order_;</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;  T knot_frequency_;</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;  std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt; data_;</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;  std::vector&lt;T&gt; time_;</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160; </div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;  <span class="comment">// Derived properties of the spline.</span></div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;  <span class="keywordtype">int</span> spline_degree_;</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;  std::vector&lt;T&gt; knots_;</div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;  std::vector&lt;T&gt; valid_knots_;</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;  Eigen::MatrixXd derivative_coeffs_;</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;  std::vector&lt;Eigen::MatrixXd&gt; Mi_;</div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;  std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt; control_points_;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160; </div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160; </div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;  <span class="comment">// Convenience function for computing a knot vector.</span></div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;  <span class="keywordtype">void</span> ComputeKnotVector();</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160; </div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;  <span class="comment">// Convenience function for computing the basis matrices for this spline.</span></div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;  <span class="keywordtype">void</span> ComputeBasisMatrices();</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160; </div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;  <span class="comment">// Methods implementing the recursive algorithm for computing the basis</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;  <span class="comment">// matrix per Theorem 1 of &quot;General Matrix Representations for B-Splines&quot;.</span></div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;  <span class="comment">//   M_k = [ M_km1 ] * A + [  0^T  ] * B</span></div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;  <span class="comment">//       = [  0^T  ]       [ M_km1 ]</span></div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;  <span class="comment">//   </span></div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;  <span class="comment">//   A = [ 1-d_0,i-k+2   d_0,i-k+2                              ]</span></div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;  <span class="comment">//       [              1-d_0,i-k+3  d_0,i-k+3                  ]</span></div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;  <span class="comment">//       [                  ...                                 ]</span></div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;  <span class="comment">//       [                                       1-d_0,i  d_0,i ]</span></div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;  <span class="comment">//    </span></div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;  <span class="comment">//   B = [ -d_1,i-k+2   d_1,i-k+2                               ]</span></div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;  <span class="comment">//       [             -d_1,i-k+3   d_0,i-k+3                   ]</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;  <span class="comment">//       [                    ...                               ]</span></div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;  <span class="comment">//       [                                      -d_1,i  d_1,i   ]</span></div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;  <span class="comment">// where k is the spline order and i is the spline segment number.</span></div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;  Eigen::MatrixX&lt;T&gt; M(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i);</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;  T d_0(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j);</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;  T d_1(<span class="keywordtype">int</span> k, <span class="keywordtype">int</span> i, <span class="keywordtype">int</span> j);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;  <span class="comment">// Fit spline to data.</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;  <span class="keywordtype">void</span> FitSpline();</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;  <span class="comment">// Check that inputs provided for spline fit are valid.</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;  absl::Status CheckDataForSplineFit(</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;      <span class="keyword">const</span> std::vector&lt;T&gt;&amp; time,</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;      <span class="keyword">const</span> std::vector&lt;Eigen::Vector&lt;T,N&gt;&gt;&amp; data, <span class="keywordtype">int</span> spline_order,</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;      T knot_frequency);</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;};</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;} <span class="comment">// namespace calico</span></div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;<span class="preprocessor">#include &quot;calico/bspline.hpp&quot;</span></div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;<span class="preprocessor">#endif </span><span class="comment">// CALICO_BSPLINE_H_</span></div>
<div class="ttc" id="aclasscalico_1_1BSpline_html"><div class="ttname"><a href="classcalico_1_1BSpline.html">calico::BSpline</a></div><div class="ttdef"><b>Definition:</b> bspline.h:17</div></div>
<div class="ttc" id="anamespacecalico_html"><div class="ttname"><a href="namespacecalico.html">calico</a></div><div class="ttdoc">Primary calico namespace.</div><div class="ttdef"><b>Definition:</b> __init__.py:1</div></div>
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